To solve the system of equations given by:
- \( 6x - 3y = -6 \)
- \( 9x - 3y = -18 \)
First, we can simplify both equations.
For the first equation: \[ 6x - 3y = -6 \] Dividing the entire equation by 3: \[ 2x - y = -2 \] or \[ y = 2x + 2 \] (Equation 1)
For the second equation: \[ 9x - 3y = -18 \] Dividing the entire equation by 3: \[ 3x - y = -6 \] or \[ y = 3x + 6 \] (Equation 2)
Now we have a simplified system:
- \( y = 2x + 2 \)
- \( y = 3x + 6 \)
Since both equations equal \( y \), we can set them equal to each other: \[ 2x + 2 = 3x + 6 \]
Now, isolate \( x \): \[ 2 = 3x - 2x + 6 \] \[ 2 = x + 6 \] Subtracting 6 from both sides: \[ 2 - 6 = x \] \[ x = -4 \]
Now, we substitute \( x = -4 \) back into one of the equations to find \( y \). We'll use Equation 1: \[ y = 2(-4) + 2 \] \[ y = -8 + 2 \] \[ y = -6 \]
Therefore, the solution to the system of equations is: \[ (x, y) = (-4, -6) \]
So the final answer is: \[ \boxed{(-4, -6)} \]